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Filters
Electronic filters are a type of in the form of electrical circuits. This article covers those filters consisting of electronic components, as opposed to s. That is, using components and interconnections that, in analysis, can be considered to exist at a single point. These components can be in discrete packages or part of an . Electronic filters remove unwanted frequency components from the applied signal, enhance wanted ones, or both. They can be: * or * or * , , , (band-rejection; notch), or . * (sampled) or * or * (IIR type) or (FIR type) The most common types of electronic filters are , regardless of other aspects of their design. See the article on linear filters for details on their design and analysis. Analogue filter Analogue are a basic building block of much used in . Amongst their many applications are the separation of an audio signal before application to , , and s; the combining and later separation of multiple telephone conversations onto a single channel; the selection of a chosen in a and rejection of others. Passive linear electronic analogue filters are those filters which can be described with s (linear); they are composed of s, s and, sometimes, s ( ) and are designed to operate on continuously varying ( ) signals. There are many s which are not analogue in implementation ( ), and there are many s which may not have a passive topology – both of which may have the same of the filters described in this article. Analogue filters are most often used in wave filtering applications, that is, where it is required to pass particular frequency components and to reject others from analogue ( ) signals. Analogue filters have played an important part in the development of electronics. Especially in the field of s, filters have been of crucial importance in a number of technological breakthroughs and have been the source of enormous profits for telecommunications companies. It should come as no surprise, therefore, that the early development of filters was intimately connected with s. Transmission line theory gave rise to filter theory, which initially took a very similar form, and the main application of filters was for use on telecommunication transmission lines. However, the arrival of techniques greatly enhanced the degree of control of the designer. Today, it is often preferred to carry out filtering in the digital domain where complex algorithms are much easier to implement, but analogue filters do still find applications, especially for low-order simple filtering tasks and are often still the norm at higher frequencies where digital technology is still impractical, or at least, less cost effective. Wherever possible, and especially at low frequencies, analogue filters are now implemented in a which is in order to avoid the wound components (i.e. inductors, transformers, etc.) required by topology. It is possible to design linear analogue s using mechanical components which filter mechanical vibrations or waves. While there are few applications for such devices in mechanics per se, they can be used in electronics with the addition of s to convert to and from the electrical domain. Indeed, some of the earliest ideas for filters were acoustic resonators because the electronics technology was poorly understood at the time. In principle, the design of such filters can be achieved entirely in terms of the electronic counterparts of mechanical quantities, with , and corresponding to the energy in inductors, capacitors and resistors respectively. Infinite impulse response Infinite impulse response (IIR) is a property applying to many s. Common examples of linear time-invariant systems are most and s. Systems with this property are known as IIR systems or IIR filters, and are distinguished by having an which does not become exactly zero past a certain point, but continues indefinitely. This is in contrast to a (FIR) in which the impulse response h''(''t) does become exactly zero at times t'' > ''T for some finite T'', thus being of finite duration. In practice, the impulse response, even of IIR systems, usually approaches zero and can be neglected past a certain point. However the physical systems which give rise to IIR or FIR responses are dissimilar, and therein lies the importance of the distinction. For instance, analog electronic filters composed of resistors, capacitors, and/or inductors (and perhaps linear amplifiers) are generally IIR filters. The capacitors (or inductors) in the analog filter have a "memory" and their internal state never completely relaxes following an impulse (assuming the classical model of capacitors and inductors where quantum effects are ignored). :On the other hand, s (usually digital filters) based on a tapped delay line ''employing no feedback are necessarily FIR filters. After an impulse has reached the end of the tapped delay line, the system has no further memory of that impulse and has returned to its initial state; its impulse response beyond that point is exactly zero. Linear phase Linear phase is a property of a , where the of the filter is a of . The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the . And consequently, there is no due to the time delay of frequencies relative to one another. For signals, perfect linear phase is easily achieved with a (FIR) filter by having coefficients which are symmetric or anti-symmetric. Approximations can be achieved with (IIR) designs, which are more computationally efficient. Several techniques are':' * a transfer function which has a maximally flat group delay approximation function * a A filter is called a linear phase filter if the phase component of the frequency response is a linear function of frequency. For a continuous-time application, the frequency response of the filter is the of the filter's , and a linear phase version has the form: : H(\omega) = A(\omega)\ e^{-j \omega \tau}, where: *A(ω) is a real-valued function. * \tau is the group delay. For a discrete-time application, the of the linear phase impulse response has the form: : H_{2\pi}(\omega) = A(\omega)\ e^{-j \omega k/2}, where: *A(ω) is a real-valued function with 2π periodicity. *k is an integer, and k/2 is the group delay in units of samples. H_{2\pi}(\omega) is a that can also be expressed in terms of the of the filter impulse response. I.e.: : H_{2\pi}(\omega) = \left. \widehat H(z) \, \right|_{z = e^{j \omega}} = \widehat H(e^{j \omega}), where the \widehat H notation distinguishes the Z-transform from the Fourier transform. Causal filter In , a causal filter is a . The word causal indicates that the filter output depends only on past and present inputs. A whose output also depends on future inputs is non-causal, whereas a filter whose output depends only on future inputs is anti-causal. Systems (including filters) that are realizable (i.e. that operate in ) must be causal because such systems cannot act on a future input. In effect that means the output sample that best represents the input at time t, comes out slightly later. A common design practice for s is to create a realizable filter by shortening and/or time-shifting a non-causal impulse response. If shortening is necessary, it is often accomplished as the product of the impulse-response with a . An example of an anti-causal filter is a filter, which can be defined as a , anti-causal filter whose inverse is also stable and anti-causal. References Category:Electronics